To obtain a metallocene catalyst system which can give an olefinically unsaturated polymer having a high molecular weight in high productivity by using a specified transition metal metallocene complex, a compound which forms metallocene ions, and a sterically hindered organic Lewis base as the effective components.

This system contains a metallocene complex (A) of a group 4, 5 or 6 transition metal in the periodic table, a compound (B) which forms metallocene ions, and a sterically hindered organic Lewis acid (C). Component B is desirably a 1-10C aluminoxane. Component C is desirably a sterically hindered hydroxyaryl compound or a sterically hindered aryloxyaluminum compound. At least two olefinically unsaturated monomers are polymerized at 0-450°C under a pressure of 0.1-500,000kPa in the presence of the catalyst system to produce a polymer.